Persistent homology of the logistic map : an exploration of chaos

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Abstract

Given a discrete sampling of points, how can one reconstruct the underlying geometric object? Further, the question arises how can one discern between noise and sampling distortion and important topological features. Algebraic and topological techniques used computationally can prove to be powerful and currently unconventional tools to understand the "shape" of data. In recent years, persistent homology has been explored as a computational way to capture information regarding the longevity of topological features of discrete data sets. In this project, the persistent homology of functions is ...(For more, see "View full record.")